Related papers: Bounded Homotopy Path Approach to Find the Solutio…
Numerical continuation methods track a solution path defined by a homotopy. The systems we consider are defined by polynomials in several variables with complex coefficients. For larger dimensions and degrees, the numerical conditioning…
In this paper, we develop a drift homotopy implicit particle filter method. The methodology of our approach is to adopt the concept of drift homotopy in the resampling procedure of the particle filter method for solving the nonlinear…
We establish universal approximation theorems for infinite-dimensional geometric rough paths, i.e., we show that continuous functions on the space of infinite-dimensional weakly geometric H\"older continuous rough paths can be approximated…
We introduce parity quantum optimization with the aim of solving optimization problems consisting of arbitrary $k$-body interactions and side conditions using planar quantum chip architectures. The method introduces a decomposition of the…
The goal of Point Distance Solving Problems is to find 2D or 3D placements of points knowing distances between some pairs of points. The common guideline is to solve them by a numerical iterative method (\emph{e.g.} Newton-Raphson method).…
We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising…
We consider the solution of initial value problems within the context of hybrid systems and emphasise the use of high precision approximations (in software for exact real arithmetic). We propose a novel algorithm for the computation of…
Qualitative methods such as the linear sampling method and the factorization method reconstruct acoustic scatterers through sampling indicators. In practice, these indicators are gray-scale fields on a prescribed sampling window and a…
In this paper, we present a neural network approach to address the dynamic unbalanced optimal transport problem on surfaces with point cloud representation. For surfaces with point cloud representation, traditional method is difficult to…
We consider a Hamiltonian decomposition problem of partitioning a regular graph into edge-disjoint Hamiltonian cycles. It is known that verifying vertex non-adjacency in the 1-skeleton of the symmetric and asymmetric traveling salesperson…
Solving Einstein's constraint equations for the construction of black hole initial data requires handling the black hole singularity. Typically, this is done either with the excision method, in which the black hole interior is excised from…
The polyhedral homotopy method of Huber and Sturmfels is a particularly efficient and robust numerical method for solving system of (Laurent) polynomial equations. A central component in an implementation of this method is an efficient and…
Despite the attention that the problem of path planning for tethered robots has garnered in the past few decades, the approaches proposed to solve it typically rely on a discrete representation of the configuration space and do not exploit…
We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We…
Despite their abundance in robotics and nature, underactuated systems remain a challenge for control engineering. Trajectory optimization provides a generally applicable solution, however its efficiency strongly depends on the skill of the…
The asymptotic Karush-Kuhn-Tucker (AKKT) optimality conditions are distinguished from other approaches in the literature by virtue of their capacity to be effectively derived through numerical methods, such as the utilization of an…
In this paper, we extend a previously presented Grover-based heuristic to tackle general combinatorial optimization problems with linear constraints. We further describe the introduced method as a framework that enables performance…
This paper presents a novel factor graph-based approach to solve the discrete-time finite-horizon Linear Quadratic Regulator problem subject to auxiliary linear equality constraints within and across time steps. We represent such optimal…
We study the path planning problem for continuum-arm robots, in which we are given a starting and an end point, and we need to compute a path for the tip of the continuum arm between the two points. We consider both cases where obstacles…
We present a new interior-point potential-reduction algorithm for solving monotone linear complementarity problems (LCPs) that have a particular special structure: their matrix $M\in{\mathbb R}^{n\times n}$ can be decomposed as $M=\Phi U +…